Problem: $\dfrac{ -2x + 5y }{ -5 } = \dfrac{ 10x - 6z }{ -2 }$ Solve for $x$.
Solution: Multiply both sides by the left denominator. $\dfrac{ -2x + 5y }{ -{5} } = \dfrac{ 10x - 6z }{ -2 }$ $-{5} \cdot \dfrac{ -2x + 5y }{ -{5} } = -{5} \cdot \dfrac{ 10x - 6z }{ -2 }$ $-2x + 5y = -{5} \cdot \dfrac { 10x - 6z }{ -2 }$ Multiply both sides by the right denominator. $-2x + 5y = -5 \cdot \dfrac{ 10x - 6z }{ -{2} }$ $-{2} \cdot \left( -2x + 5y \right) = -{2} \cdot -5 \cdot \dfrac{ 10x - 6z }{ -{2} }$ $-{2} \cdot \left( -2x + 5y \right) = -5 \cdot \left( 10x - 6z \right)$ Distribute both sides $-{2} \cdot \left( -2x + 5y \right) = -{5} \cdot \left( 10x - 6z \right)$ ${4}x - {10}y = -{50}x + {30}z$ Combine $x$ terms on the left. ${4x} - 10y = -{50x} + 30z$ ${54x} - 10y = 30z$ Move the $y$ term to the right. $54x - {10y} = 30z$ $54x = 30z + {10y}$ Isolate $x$ by dividing both sides by its coefficient. ${54}x = 30z + 10y$ $x = \dfrac{ 30z + 10y }{ {54} }$ All of these terms are divisible by $2$ $x = \dfrac{ {15}z + {5}y }{ {27} }$